Question

How do you convert radian measures to degrees?

Answer 1

`"see explanation"`

Explanation:

`"to convert from "color(blue)"radians to degrees"`

`color(red)(bar(ul(|color(white)color(black)("degrees "="radians "xx180^@/pi)color(white)(2/2)|)))`

`"to convert from "color(blue)"degrees to radians"`

`color(red)(bar(ul(|color(white)(2/2)color(black)("radians "="degrees "xxpi/180^@)color(white)(2/2)|)))`

Answer 2

Throug the equivalence `pi=180º` and de direct proportionality of arcs and angles. See examples

Explanation:

If we have 45º degrees convert to radians is easy

`pi/x=180/45`. Then `x=(45pi)/180=pi/4`. So `45º=pi/4 rad`

By the other hand, if we have `pi/3` rads, to convert to degrees, we use the same equivalence

`pi/(pi/3)=180/y`. Trasposing terms `y=(180pi)/(3pi)=180/3=60º`